In Greek we mostly use the fossilized expression from Ancient Greek «κατά κόρον*» [ka'ta 'koron] --> to the surfeit [of it]. A more modern approach (and a colloquialism) to the Latin expression is «μέχρι αηδίας**» ['mexri ai'ðias] --> to the point of disgust

Well, you have something similar in AE: "shop till you drop" or "dance till you die". I think "till you drop" might be a close equivalent. It makes me sick -- would be another expression. It may also mean something else in another context, but it may fit here as well.